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The Normal Inverse Gaussian Distribution for Synthetic CDO Pricing

by Anna Kalemanova of Risklab Germany,
Bernd Schmid of UBS Investment Bank, and
Ralf Werner of Hypo Real Estate Holding, AG

January 2007

Abstract: This paper presents an extension of the popular Large Homogeneous Portfolio (LHP) approach to the pricing of CDOs. LHP (which has already become a standard model in practice) assumes a flat default correlation structure over the reference credit portfolio and models defaults using a one factor Gaussian copula. However, this model fails to fit the prices of different CDO tranches simultaneously which leads to the well known implied correlation skew. Many researchers explain this phenomenon with the lack of tail dependence in the Gaussian copula and propose to use a Student t-distribution. Incorporating the effect of tail dependence into the one factor portfolio credit model yields significant pricing improvement. However, the computation time increases dramatically as the Student t-distribution is not stable under convolution. This makes it impossible to use the model for computationally intensive applications such as the determination of the optimal asset allocation in an investor's portfolio over different asset classes including CDOs. We present a modification of the LHP model replacing the Student t-distribution with the Normal inverse Gaussian (NIG) distribution. We compare the properties of our new model with those of the Gaussian and the double t-copulas. The employment of the NIG distribution not only speeds up the computation time significantly but also brings more flexibility into the dependence structure.

Keywords: CDO, correlation smile, copula, factor model, large homogeneous portfolio, normal inverse Gaussian.

Published in: Journal of Derivatives, Vol. 14, No. 3, (Spring 2007), pp. 80-93.

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